Inverting amplitude and phase to reconstruct tip-sample interaction forces in tapping mode atomic force microscopy

Quantifying the tip-sample interaction forces in amplitude-modulated atomic force microscopy (AM-AFM) has been an elusive yet important goal in nanoscale imaging, manipulation and spectroscopy using the AFM. In this paper we present a general theory for the reconstruction of tip-sample interaction forces using integral equations for AM-AFM and Chebyshev polynomial expansions. This allows us to reconstruct the tip-sample interactions using standard amplitude and phase versus distance curves acquired in AM-AFM regardless of tip oscillation amplitude and in both the net attractive and repulsive regimes of oscillation. Systematic experiments are performed to reconstruct interaction forces on polymer samples to demonstrate the power of the theoretical approach